Gas-liquid Interaction Research Articles

Mathematical Modeling of Iron and Steel Making Pocesses. Modelling of Liquid Flow in the Blast Furnace. Theoretical Analysis of the Effects of Gas, Liquid and Packing Properties.

Molten iron and slag flows play a critical role in the blast furnace lower zone, transporting mass and energy, whilst impairing and redistributing gas flow. In turn, molten iron and slag undergo physical and chemical changes, and are redistributed radially during descent to the hearth. Using a 'force-balance' approach, the flows of liquid in the blast furnace were characterised. A consistent set of equations describing liquid holdup, gas–liquid interaction and solid–liquid interaction was developed with reference to previous experimental studies and furnace conditions. The model accounts for the effect of gas, liquid and packing properties on liquid flow, as well as the effect of liquid on gas flow. Interaction between metal and slag phases occurs via a shared gas flow field. Importantly, the model can be applied under both countercurrent and non-countercurrent conditions, where gas can either hinder or enhance liquid flow.

Numerical modeling of wavy stratified two-phase flow in pipes

The paper presents the numerical modeling of stratified flow in circular cross-section pipe. Due to the geometry of this two-phase flow, the equations of the problem are derived in bipolar coordinate system. Above the waves, the gas flow structure is three dimensional, since secondary flows are induced by the non-uniformity of boundary conditions related to smooth wall and wavy or rough interface. The secondary flows being generated by the anisotropy of the turbulence, an algebraic stress model is used in the gas flow model. The roughness of the interface is determined from experiments. Given vertical profiles of longitudinal velocity in the gas and assuming a classical logarithmic law above the waves, it is possible to determine the magnitude of the interfacial roughness. These experimental values are imposed in the numerical simulations. Given these values, the comparison between experimental profiles and computed ones is shown to be satisfactory. Hence, the simulations validate the concept of interfacial roughness to account for gas–liquid interactions. Finally, the interfacial roughness are non-dimensionalized following Charnock proposal and its order of magnitude to be imposed in the numerical simulations is given.

A non-equilibrium phenomenological theory of the mass and heat transfer in physical and chemical interactions: Part II — modeling of the NH 3/H 2O bubble absorption, analytical study of absorption and experiments

A non-equilibrium phenomenological theory of mass and heat transfer, presented in previous works, is applied here in combination with the classical equilibrium phenomenological theory to model absorption of the ammonia bubble. The modeling tool is a non-empirical linear Phenomenological Hydro-Gaso-Dynamical (PhHGD) approach, outlined in the second section of this paper. First results refer to the elucidation of the problem of the ammonia bubble absorption, where from the following we are to be learned: (i) absorption process in the ammonia/water medium is a mass phenomenon and not a surface one; (ii) an intensive way of improving absorption is emphasized, which seeks to promote the i.p.a. effect appearance; this would replace the extensive way currently used, based on increasing gas–liquid interaction area; to this extent, the bubble absorber is hereby proposed for efficient absorption; (iii) the i.p.a. effect existence offers an additional chance for a satisfactory explanation of the Marangoni effect. The PhHGD code is extended to a refined analytical study of absorption, which may constitute a first data base for the bubble absorber. The paper also presents experimental results of ammonia bubble absorption in water, which are in good agreement with the predictions of the PhHGD approach.

A non-equilibrium phenomenological theory of the mass and heat transfer in physical and chemical interactions: Part I — application to NH 3/H 2O and other working systems

The paper presents an original non-equilibrium phenomenological theory of mass and heat transfer. The theory is particularized to a few case studies including physical binary gas–liquid interactions in non-ideal mixtures (e.g., working system NH 3/H 2O), pure components (NH 3, H 2O), as well as an independent chemical interaction (ammonia synthesis). All applications emphasize an important feature of the mass and heat coupled currents, that is the ideal point approaching (i.p.a.) effect, not mentioned so far in the specialized literature. The i.p.a. effect consists of a continuous increase of the mass and heat currents of an interaction evolving towards an ideal point, by several percentages (pure component case) to several hundreds of times (working pairs case), as compared to the states which are far from the same ideal point. On the contrary, the forces of systems with non-coupled mass and heat currents tend to zero when evolve to equilibrium. The paper raises the problem of the ammonia bubble absorption, not satisfactorily explained by the ‘two films’ theory. The existence of the i.p.a. effect satisfactorily explains it from a qualitative point of view. This explanation throws a new light on the absorption phenomenon encountered by the working pairs used in the thermal absorption technology: (i) absorption process is not a surface phenomenon, as it is usually considered and (ii) the actual estimation of the interface mass transfer by analogy with heat transfer is improper. The non-equilibrium approach, outlined in this paper, is not contradictory to the classic equilibrium phenomenological theory. On the contrary, it may be an equivalent alternative or it may be combined with the classic approach in order to assess mass and heat transfer processes. Its main investigation tool, the natural thermodynamical force, has specific important features in the neighbourhood of an ideal point.

A phenomenological theory of polycomponent interactions in non-ideal mixtures. Application to NH 3/H 2O and other working pairs

The paper proposes an original linear phenomenological theory (Ph T) of evolution physical mono-, bi- and particular polycomponent gas–liquid interactions with non-ideal mixture. The expressions of the phenomenological factors (entropy source, force, coefficient and coupled heat and mass transfer currents) are deduced. The theory is particularized to the NH 3/H 2O and other gas–liquid systems used in the thermal absorption technology. The work's conclusions are listed next. The paper raises the problem of ammonia bubble absorption which is difficult to answer with current theory of interface mass transfer and absorption as a surface phenomenon. The heat and mass transfer at the gas–liquid interface is governed by the thermodynamic force, which applies also to solid–liquid, solid–gas, or liquid–liquid, gas–gas type interactions and continuous or discontinuous media. The paper mentions a postulate referring to the force behavior approaching an ideal point, previously formulated by the author. According to its consequence, the mass and heat currents suffer an ideal point approaching (i.p.a.) effect, not mentioned so far in the specialized literature, consisting in a continuous increase of their absolute value by several percent (for a pure component), to several hundred times (for a binary system) when the interacting system approaches an ideal state, as compared to the values of states which are far from the same ideal point. In this way, “far from equilibrium” becomes synonymous to “low interaction”. The classic assessment of the interface mass transfer by analogy with heat transfer lacks basic physics. The (Ph T) satisfactorily explains the problem of ammonia bubble absorption. Absorption is a mass phenomenon, not a surface one. An intensive way of improving absorption is emphasized, which seeks to promote the i.p.a. effect appearance rather than the extensive way currently used, based on increasing gas–liquid interaction area. To this extent, the bubble absorber is hereby proposed for efficient absorption. The i.p.a. effect existence offers an additional chance for a satisfactory explanation of the Marangoni effect.

Experimental Investigation of Swirl and Non-Swirl Gas Injections Into Liquid Baths Using Submerged Vertical Lances

The behaviour of the flow of swirl and non-swirl gas injections into a liquid bath was investigated experimentally, using water as modelling fluid to gain an understanding of the mixing process of the Sirosmelt top submerged gas injection system. The effects of swirl intensity, gas injection rates and lance submergence levels on the gas-liquid interaction were determined by measuring the velocity fields and the generation of turbulence in the bath. The results indicate that the swirl gas injection promoted high liquid velocities and high turbulent kinetic energy and hence better mixing in the tank. When two-thirds of the lance was submerged better mixing and high liquid velocities resulted for both gas injection rates investigated. The applicability of the concept of isotropic turbulence for the liquid bath was examined. It was found that the assumption of isotropic turbulence may hold outside the plume region. However, there are a clear indication that turbulence is non-isotropic in the vicinity of the wall region. These findings have implications in the mathematical modelling of gas injection processes.On a étudié expérimentalement le comportement d'écoulement d'injections de gaz, avec et sans tourbillon, dans un bain liquide. On a utilisé des modèles aqueux afin d'obtenir un aperçu du procédé de mélange du système Sirosmelt submergé d'injection de gaz, par le haut. On a déterminé l'effet de l'intensité du tourbillon, des taux d'injection de gaz et des niveaux d'immersion de la lance sur l'interaction gaz-liquide en mesurant les champs de vitesse et la génération de turbulence dans le bain. Les résultats semblent montrer que l'injection de gaz avec tourbillon stimulait des vitesses élevées dans le liquide et une énergie cinétique turbulente élevée et, ainsi, un meilleur mélange dans le réservoir. Les taux élevés d'injection de gaz, comme on s'y attendait, ont produit des vitesses élevées du liquide dans tout le réservoir. L'immersion aux deux tiers de la lance a résulté en un meilleur mélange et en des vitesses élevées du liquide, aux deux taux d'injection de gaz étudiés. On a examiné l'applicabilité au bain liquide du concept de turbulence isotrope. On a trouvé que l'assomption de turbulence isotrope pouvait être retenue en dehors de la région d'injection. Il y a cependant des indications claires que, dans le voisinage de la paroi, la turbulence est non-isotrope. Ces découvertes ont des implications sur la modélisation mathématique des procédés d'injection de gaz.

2413 粒子法による流動様式の研究

We have developed the two-phase flow analysis method without experimental correlations based on the Moving Particle Semi-implicit (MPS) method which is formulated by representing the differential operators in Navier-Stokes equation as the interaction between particles characterized with a kernel function. We extended MPS method to two-fluid system and introduced a surface tension model and a modified kernel for gas-liquid interaction. To verify this extended method, we analyzed experiments on void fraction distribution in a rectangular pipe, void fraction distribution change in micro-gravity condition, Lockhart-Martinelli's pressure drop correlations, pool flow regime map, and boiling behavior in a pipe. Calculation results in each case compared well with its experimental data.

A two-fluid hydrodynamic model for the transition between trickle and pulse flow in a cocurrent gas–liquid packed-bed reactor

A one-dimensional hydrodynamic model of cocurrent gas–liquid downflow through packed-bed reactors operating in the trickle flow regime is developed on the basis of a mechanistic approach. The formulation of the two-fluid model involves the mass and momentum balance equations of each fluid averaged over the void cross-sectional area of the reactor, as well as an additional equation for the capillary pressure gradient deduced from a momentum balance analysis at the gas–liquid interface. The velocity profiles for the two fluids are assumed uniform over the whole reactor cross-section. The particle–liquid and gas–liquid interactions and the column wall friction force are evaluated from closure equations based on the assumption of an annular pattern for which the gas and liquid phases are completely separated by a smooth interface, and the packing surface as well as the column wall are totally wetted by a liquid film. The linear stability analysis of the solution of the proposed hydrodynamic model around an equilibrium steady state is applied for obtaining the condition of transition to the pulsing regime. The predictions of the trickling-to-pulsing transition given from the present model and from the existing methods are compared with a large set of experimental data of the literature covering a wide range of operating conditions, fluids properties and packing characteristics. The two-fluid model is found to be able to predict the influences of the various parameters such as the physical properties of fluids, the operating conditions and the packing characteristics in qualitative agreement with the experimental trends. The accuracy of the proposed model is found to be better than the ones of the existing methods.

Uptake of Gas-Phase Ammonia. 1. Uptake by Aqueous Surfaces as a Function of pH

The uptake of gas-phase ammonia by aqueous surfaces was measured as a function of temperature, gas liquid interaction time, and pH in the range 0−13. Uptake measurements at low pH yielded values of the mass accommodation coefficient (α) as a function of temperature. The mass accommodation coefficient increases as the temperature decreases, from 0.08 at 290 K to 0.35 at 260 K. Time dependence of the uptake yielded values for the Henry's law constant. Uptake measurements at high pH indicate that an ammonia surface complex is formed at the interface. Codeposition studies in which an aqueous surface, initially at pH = 4, was simultaneously exposed to both gas-phase ammonia and SO2 were also performed. In such a codeposition experiment, the species entering the liquid neutralize each other and as a result the uptake of each species is enhanced. Modeling calculations indicate that the uptake of each species is in accord with bulk liquid-phase kinetics.

A two-fluid model for flow regime transition in gas–liquid trickle-bed reactors

A hydrodynamic model for cocurrent gas–liquid downward flow through a packed-bed reactor operating in trickle flow regime is developed. The model involves area-averaged mass and momentum balance equations of each fluid as well as an expression for the capillary pressure gradient deduced from a momentum balance analysis at the gas–liquid interface. The liquid–solid and gas–liquid interaction forces are formulated on the basis of the Kozeny–Carman equation by taking into account the presence of liquid films and the gas–liquid slip motion. The linear stability analysis of the solution of the proposed model around an equilibrium steady state is applied for obtaining the trickling-to-pulsing transition curve. The theoretical predictions of the trickling-to-pulsing transition are compared favourably with a set of experimental data corresponding to a wide range of operating conditions, fluids properties and packing characteristics.

A simple model for pressure drop and liquid hold-up in packed-bed bubble reactors

A simple hydrodynamic model for cocurrent gas–liquid bubbly flow through a packed-bed reactor is developed. The model involves the momentum balance equations for the continuous liquid phase and for the dispersed bubble phase. The liquid–solid interaction force is formulated on the basis of the Kozeny–Carman equation by taking into account the presence of bubbles reducing the available volume for the flowing liquid. The gas–liquid interaction force is evaluated by using the respective solutions of drag coefficient for an isolated bubble in the viscous and Newton regimes. For each regime, a correction is effected to the bubble drag coefficient to take into account the presence of a large number of bubbles. The theoretical predictions of pressure drop and liquid hold-up are compared favourably with experimental data of the literature obtained for the upward and downward packed-bed bubble reactors.

A Model for Pressure Drop of Gas-Liquid Bubbly Flow through an Orifice or an Abrupt Pipe Contraction

A new physical model is developed to predict the pressure drop of a steady-state gas-liquid bubbly flow through an orifice or an abrupt pipe contraction. The formulation of the model involves balance equations deduced from the macroscopic mass, momentum, entropy and energy conservation laws as well as a balance of forces exerted on the dispersed bubbles phase. The thermal equilibrium between phases is assumed but the gas-liquid slip motion is taken into account. The gas-liquid interaction and the wall shear stress are evaluated from theoretical considerations. The predictions of pressure drop from the model are found to be in good agreement with several experimental data of the literature obtained for bubbly air-water flows through orifices. In agreement with the experimental observations, the theoretical predictions show that the two-phase pressure drop multiplier is not strongly influenced by the pipe diameter and increases slightly with the cross-sectional area ratio of the orifice. An essential feature of the present model is the absence of adjustable constants.

Modelling of the hydrodynamics of the cocurrent gas–liquid trickle flow through a trickle-bed reactor

A physical model is developed to predict the hydrodynamic parameters of steady-state cocurrent gas–liquid flow through trickle-bed reactors operating in the trickle flow regime. The trickle flow is described by an annular pattern in which the gas and liquid phases are completely separated by a smooth and stable interface. The formulation of the model involves balance equations deduced from the macroscopic mass and momentum conservation laws. The particle–liquid drag and the gas–liquid interactions, i.e. the gas–liquid drag due to the relative motion between the fluids and the force by which the gas pushes the liquid against the solid particles, are evaluated from theoretical considerations. The predictions of the liquid saturation and pressure gradient from the model are found to be in good agreement with existing experimental data obtained in a wide range of operating pressure (0.1–10 MPa) for various gas–liquid and packing systems. The present model predicts these two hydrodynamic parameters with a better accuracy than the available correlation ones. Some underestimation of the pressure gradient is observed for the highest values of the superficial gas velocity and operating pressure due to the droplets entrainment and the wavy pattern of the gas–liquid interface that are not taken into account. The fundamental feature of the present model is the total absence of adjustable constants.

Hydrodynamics in a Pressurized Cocurrent Gas-Liquid Trickle-Bed Reactor: A Physical Model

A physical model describing the hydrodynamics in a steady-state pressurized cocurrent gas-liquid trickle-bed reactor is presented. The gas-liquid trickle-flow is modeled by an annular pattern in which the gas and liquid phases are separated by a smooth and stable interface. The formulation of the model involves the macroscopic mass and momentum balance equations applied to the gas and liquid phases. The particle-liquid and gas-liquid interactions are evaluated on the basis of the Ergun equation. Comparisons with the experimental data of the pressure gradient and liquid saturation obtained in a large range of operating pressure show that the predictions from this model are more accurate that the ones given from the available correlations. However, it can not be applied to packed beds characterized by a column diameter over the particle diameter ratio D/d p of less than 12-14 due to the wall effect.

A numerical method for determining the kinetic constants of gas–liquid metal interactions in N–Ni–20Cr and N–ASTM F-75 alloy systems

In gas–liquid interaction systems, under non-equilibrium degassing conditions, the rate of a particular process often follows a mixed control regime where serial-acting mechanisms affect the global rate of the process and, therefore, the determination of real kinetic constants is difficult. In this paper a numerical method for determining these kinetic constants is presented and applied to the cases of denitrogenation of liquid Ni–20Cr alloys at 1873 K and nitrogen absorption in liquid ASTM F-75 alloys at 1773 and 1823 K. The results showed that interaction kinetics of nitrogen with both alloys was limited by both first and second order mechanisms. This results permit manufacturing engineers to act on the process parameters in order to obtain the nitrogen content that allows the best performance of mechanical parts.

Scale and variance of radial liquid maldistribution in trickle beds

Radial distribution of liquid flow rate in a trickle bed with an inner diameter of 0.283 m was measured for various bed heights under varying flow conditions. The total variance of flow distribution was partitioned into large-scale and small-scale components, and the statistical method was used to analyze the experimental data and determine the scale of liquid maldistribution. The scale of nonuniform radial distribution varied from 0.02 to 0.3 m as indicated by diagrams of the power spectral density function (PSDF). Both scale and variance of small-scale maldistribution decrease as gas and liquid flow rates are increased, suggesting that maldistribution is mainly governed by gas–liquid interaction. On the contrary, large-scale liquid maldistribution (wall flow and central flow) was dominantly controlled by solid–liquid interaction. The experimental results also showed close relationship between some hydrodynamic phenomena and liquid distribution.

Prediction of pressure drop and liquid saturation in trickle-bed reactors operated in high interaction regimes

Simple models, based on liquid-solid and gas-liquid interaction are proposed in order to model a gas-liquid flow in trickle-bed reactors operating in high interaction regimes. Good results are obtained, when the liquid-solid and the gas-liquid interactions are modeled separately. Besides the classical Ergun equation, a simple model of the liquid-solid interactions, based on a boundary layer flow is proposed. This approach results in a relation which is very close to the well-known liquid saturation correlation proposed by Specchia and Baldi (1977, Chem. Engng Sci.32, 515–523), and might be its theoretical justification. The gas-liquid interaction is modeled using a drift-flux approach. The different models are tested against the data bank of about 1500 saturation and pressure drop measurements, established mainly by the Nancy research group. The importance of the geometrical characteristics of the porous media and their incomplete description are emphasized. Finally simple predictive correlations based on the models are proposed, tested against the data bank and compared to literature correlations.

On the eigenfrequency of a gas bubble in a liquid

This investigation concerns free linear gas bubble oscillations in liquids. Of prime interest is the eigenfrequency, and in particular its real part, here named as the transient frequency. The conceptual difference between the more frequently consulted resonance frequency and the transient frequency is first addressed by means of the classical mechanical oscillator. Next, bubble pulsations in liquids are discussed and an existing model is used for the gas–liquid interaction from which an approximate expression for the eigenfrequency is derived. A rationale for the approximate evaluation of the functions modeling the thermal processes is suggested which is independent of the frequency content of any possible pressure excitation. Moreover, compressibility effects are not approximated in the derivation presented here. The quantitative difference between the adiabatic resonance frequency and the derived estimate of the transient frequency is found to be of significance for small bubbles. Finally, the similarity between a standard mechanical oscillator and a bubble in a liquid for the case of liquid-compressibility effects only is discussed.

Horizontal Bubble Train Apparatus for Heterogeneous Chemistry Studies: Uptake of Gas-Phase Formaldehyde

A new horizontal bubble train apparatus has been built to conduct time-resolved gas−liquid interaction studies of interest in atmospheric chemistry. In the apparatus, liquid is pumped horizontally through a 0.4 cm i.d. quartz tube at a controlled speed of 15−35 cm/s. A low-pressure (about 50 Torr) gas flow, carrying the trace gas of interest diluted in helium carrier gas, is injected through a moveable injector into the liquid flow forming well-defined bubbles that fill the diameter of the tube. In a controlled way, 10−25 bubbles are formed per second. The outlet gas flow is then sampled by a differentially pumped mass spectrometer. The position of the bubble injector, which is computer controlled by a stepping motor, determines the bubble travel distance and therefore the gas-liquid interaction time (typically 0.1−10 s). Modeling of the gas uptake and the validation of the apparatus performance are described. The apparatus can measure Henry's law coefficients (H) for non-reactive species in the range 10-...

Model Study of Liquid Flow in the Blast Furnace Lower Zone.

Countercurrent gas-liquid interactions in the lower zone of a blast furnace play an important role in achieving stable operations with high productivity and efficiency. Previous gas-liquid flow models for the blast furnace did not adequately consider both the discrete nature of liquid flow and the strong, localised gas-liquid interactions occurring in the cohesive zone, which have been elucidated experimentally. The present work details a two-dimensional numerical model and a cold two-dimensional physical model, used to study gas-liquid flow in the blast furnace cohesive zone. The numerical model utilises a force balance approach to describe the discrete liquid flow and a stochastic treatment to take into account the complex packing structure. The validity of this model was demonstrated by the good agreement between model predictions and experimental observations. The model can be applied to simulate gas-liquid two-phase flow in a layered packing with multiple liquid sources, similar to the blast furnace lower zone condition.